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Plasma (from Ancient Greek πλάσμα, meaning "moldable substance"[1]) is a state of matter in which an ionised gaseous substance becomes highly electrically conductive to the point that long-range electric and magnetic fields dominate the behavior of the matter. It is one of the four fundamental states of matter, and was first described by chemist Irving Langmuir[2] in the 1920s.[3]. Unlike the other three states of solid, liquid, and gas, plasma does not freely exist on the Earth under normal surface conditions, and can only be artificially generated by heating neutral gases or by subjecting that gas to a strong electromagnetic field.[4]

Plasma
Lightning3.jpg NeTube.jpg
Plasma-lamp 2.jpg Space Shuttle Atlantis in the sky on July 21, 2011, to its final landing.jpg
Top: Lightning and neon lights are commonplace generators of plasma. Bottom left: A plasma globe, illustrating some of the more complex plasma phenomena, including filamentation. Bottom right: A plasma trail from the Space Shuttle Atlantis during re-entry into Earth's atmosphere, as seen from the International Space Station.

Plasma and ionised gases have unique properties and display behaviors unlike those of the other states, and the transition between them is mostly a matter of nomenclature[2] and subject to interpretation.[5] Based on the surrounding environmental temperature and density, partially ionised or fully ionised forms of plasma may be produced. Neon signs or lightning storms are examples of partially ionised plasma,[6] while the interior of the Sun is an example of fully ionised plasma,[7] along with the solar corona[8] and stars.[9]

The positive charge in ions is achieved by stripping away electrons from atomic nuclei. The number of electrons removed is related to either the increase in temperature or the local density of other ionised matter. This also can be accompanied by the dissociation of molecular bonds,[10] though this process is distinctly different from chemical processes of ion interactions in liquids or the behavior of ions existing in metals. The response of plasma to electromagnetic fields can be usefully employed in many modern technological devices, such as plasma televisions or plasma etching.[11]

Plasma may be the most abundant form of ordinary matter in the universe,[12] although this hypothesis is currently tentative based on the existence and unknown properties of dark matter. Plasma is mostly associated with stars, extending to the rarefied intracluster medium and possibly the intergalactic regions.[13]

Contents

HistoryEdit

The word plasma comes from the Ancient Greek πλάσμα, meaning "moldable substance"[1] or "jelly",[2] whose usage describes the behaviour of the ionised atomic nuclei and the electrons within the surrounding region of the plasma. Very simply, each of these nuclei are suspended in a movable sea of electrons. Plasma was first identified in a Crookes tube, and so described by Sir William Crookes in 1879 (he called it "radiant matter").[14] The nature of this "cathode ray" matter was subsequently identified by British physicist Sir J.J. Thomson in 1897.[15]

The term "plasma" was coined by Irving Langmuir in 1928.[16] Lewi Tonks and Harold Mott-Smith, both of whom worked with Irving Langmuir in the 1920s, recall that Langmuir first used the word "plasma" in analogy with blood.[17][18] Mott-Smith recalls, in particular, that the transport of electrons from thermionic filaments reminded Langmuir of “the way blood plasma carries red and white corpuscles and germs.”[19]

Langmuir described the plasma he observed as follows:

"Except near the electrodes, where there are sheaths containing very few electrons, the ionised gas contains ions and electrons in about equal numbers so that the resultant space charge is very small. We shall use the name plasma to describe this region containing balanced charges of ions and electrons."[16]

Properties and parametersEdit

 
Artist's rendition of the Earth's plasma fountain, showing oxygen, helium, and hydrogen ions that gush into space from regions near the Earth's poles. The faint yellow area shown above the north pole represents gas lost from Earth into space; the green area is the aurora borealis, where plasma energy pours back into the atmosphere.[20]

DefinitionEdit

Plasma is a state of matter in which an ionised gaseous substance becomes highly electrically conductive to the point that long-range electric and magnetic fields dominate the behavior of the matter.[21][22] This state can be contrasted with the other states: solid, liquid, and gas. Unlike these other states of matter, plasma mostly does not naturally exist on the Earth's surface under normal conditions, and must be artificially generated from neutral gases.[4]

Plasma is an electrically neutral medium of unbound positive and negative particles (i.e. the overall charge of a plasma is roughly zero). Although these particles are unbound, they are not ‘free’ in the sense of not experiencing forces. Moving charged particles generate an electric current within a magnetic field, and any movement of a charged plasma particle affects and is affected by the fields created by the other charges. In turn this governs collective behavior with many degrees of variation.[10][23] Three factors define a plasma:[24][25]

  1. The plasma approximation: The plasma approximation applies when the plasma parameter, Λ,[26] representing the number of charge carriers within a sphere (called the Debye sphere whose radius is the Debye screening length) surrounding a given charged particle is sufficiently high so as to shield the electrostatic influence of the particle outside of the sphere.[21][22]
  2. Bulk interactions: The Debye screening length (defined above) is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, where boundary effects may take place. When this criterion is satisfied, the plasma is quasineutral.[27]
  3. Plasma frequency: The electron plasma frequency (measuring plasma oscillations of the electrons) is large compared to the electron-neutral collision frequency (measuring frequency of collisions between electrons and neutral particles). When this condition is valid, electrostatic interactions dominate over the processes of ordinary gas kinetics.[28]

Degree of ionisationEdit

For plasma to exist, ionization is necessary. The term "plasma density" by itself usually refers to the "electron density", that is, the number of free electrons per unit volume. The degree of ionization of a plasma is the proportion of atoms that have lost or gained electrons, and is controlled mostly by the temperature. Even a partially ionised gas in which as little as 1% of the particles are ionised can have the characteristics of a plasma (i.e., response to magnetic fields and high electrical conductivity). The degree of ionization,  , is defined as  , where   is the number density of ions and   is the number density of neutral atoms. The electron density is related to this by the average charge state   of the ions through  , where   is the number density of electrons.

TemperaturesEdit

Plasma temperature is commonly measured in kelvins or electronvolts and is, informally, a measure of the thermal kinetic energy per particle. High temperatures are usually needed to sustain ionization, which is a defining feature of a plasma. The degree of plasma ionization is determined by the electron temperature relative to the ionization energy (and more weakly by the density), in a relationship called the Saha equation. At low temperatures, ions and electrons tend to recombine into bound states—atoms[29]—and the plasma will eventually become a gas.

In most cases the electrons are close enough to thermal equilibrium that their temperature is relatively well-defined, even when there is a significant deviation from a Maxwellian energy distribution function, for example, due to UV radiation, energetic particles, or strong electric fields. Because of the large difference in mass, the electrons come to thermodynamic equilibrium amongst themselves much faster than they come into equilibrium with the ions or neutral atoms. For this reason, the ion temperature may be very different from (usually lower than) the electron temperature. This is especially common in weakly ionised technological plasmas, where the ions are often near the ambient temperature.

Thermal vs. nonthermal plasmasEdit

Based on the relative temperatures of the electrons, ions and neutrals, plasmas are classified as "thermal" or "non-thermal". Thermal plasmas have electrons and the heavy particles at the same temperature, i.e. they are in thermal equilibrium with each other. Nonthermal plasmas on the other hand have the ions and neutrals at a much lower temperature (sometimes room temperature), whereas electrons are much "hotter" ( ).[30]

Complete vs. incomplete ionizationEdit

A plasma is sometimes referred to as being "hot" if it is nearly fully ionised, or "cold" if only a small fraction (for example 1%) of the gas molecules are ionised, but other definitions of the terms "hot plasma" and "cold plasma" are common. Even in a "cold" plasma, the electron temperature is still typically several thousand degrees Celsius. Plasmas utilized in "plasma technology" ("technological plasmas") are usually cold plasmas in the sense that only a small fraction of the gas molecules are ionised.[31]

Plasma potentialEdit

 
Lightning is an example of plasma present at Earth's surface. Typically, lightning discharges 30,000 amperes at up to 100 million volts, and emits light, radio waves, X-rays and even gamma rays.[32] Plasma temperatures in lightning can approach 28,000 K (28,000 °C; 50,000 °F) and electron densities may exceed 1024 m−3.

Since plasmas are very good electrical conductors, electric potentials play an important role.[clarification needed] The potential as it exists on average in the space between charged particles, independent of the question of how it can be measured, is called the "plasma potential", or the "space potential". If an electrode is inserted into a plasma, its potential will generally lie considerably below the plasma potential due to what is termed a Debye sheath. The good electrical conductivity of plasmas makes their electric fields very small. This results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma ( ), but on the scale of the Debye length there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths.[citation needed]

The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann relation:

 

Differentiating this relation provides a means to calculate the electric field from the density:

 

It is possible to produce a plasma that is not quasineutral. An electron beam, for example, has only negative charges. The density of a non-neutral plasma must generally be very low, or it must be very small, otherwise it will be dissipated by the repulsive electrostatic force.[33]

In astrophysical plasmas, Debye screening prevents electric fields from directly affecting the plasma over large distances, i.e., greater than the Debye length. However, the existence of charged particles causes the plasma to generate, and be affected by, magnetic fields. This can and does cause extremely complex behavior, such as the generation of plasma double layers, an object that separates charge over a few tens of Debye lengths. The dynamics of plasmas interacting with external and self-generated magnetic fields are studied in the academic discipline of magnetohydrodynamics.[34]

MagnetizationEdit

Plasma with a magnetic field strong enough to influence the motion of the charged particles is said to be magnetized. A common quantitative criterion is that a particle on average completes at least one gyration around the magnetic field before making a collision, i.e.,  , where   is the "electron gyrofrequency" and   is the "electron collision rate". It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are anisotropic, meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to the high conductivity, the electric field associated with a plasma moving in a magnetic field is given by   (where   is the electric field,   is the velocity, and   is the magnetic field), and is not affected by Debye shielding.[35]

Comparison of plasma and gas phasesEdit

Plasma is often called the fourth state of matter after solid, liquids and gases, despite plasma typically being an ionised gas.[36][37][38] It is distinct from these and other lower-energy states of matter. Although it is closely related to the gas phase in that it also has no definite form or volume, it differs in a number of ways, including the following:

Property Gas Plasma
Electrical conductivity Very low: Air is an excellent insulator until it breaks down into plasma at electric field strengths above 30 kilovolts per centimeter.[39] Usually very high: For many purposes, the conductivity of a plasma may be treated as infinite.
Independently acting species One: All gas particles behave in a similar way, influenced by gravity and by collisions with one another. Two or three: Electrons, ions, protons and neutrons can be distinguished by the sign and value of their charge so that they behave independently in many circumstances, with different bulk velocities and temperatures, allowing phenomena such as new types of waves and instabilities.
Velocity distribution Maxwellian: Collisions usually lead to a Maxwellian velocity distribution of all gas particles, with very few relatively fast particles. Often non-Maxwellian: Collisional interactions are often weak in hot plasmas and external forcing can drive the plasma far from local equilibrium and lead to a significant population of unusually fast particles.
Interactions Binary: Two-particle collisions are the rule, three-body collisions extremely rare. Collective: Waves, or organized motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces.

Plasmas in astronomy and astrophysicsEdit

Plasmas are by far the most common phase of ordinary matter in the universe, both by mass and by volume.[40]

Within our Solar System, interplanetary space is filled with the plasma expelled via the solar wind, extending from the Sun's surface out to the heliopause. Furthermore, all the distant stars, and much of interstellar space or intergalactic space is also likely filled with plasma, albeit at very low densities. Astrophysical plasmas are also observed in Accretion disks around stars or compact objects like white dwarfs, neutron stars, or black holes in close binary star systems.[41] Plasma is associated with ejection of material in astrophysical jets, which have been observed with accreting black holes[42] or in active galaxies like M87's jet that possibly extends out to 5,000 light-years.[43]

Common plasmasEdit

Plasmas can appear in nature in various forms and locations, which can be usefully broadly summarised in the following Table:

Common forms of plasma
Artificially produced Terrestrial plasmas Space and astrophysical plasmas

Complex plasma phenomenaEdit

Although the underlying equations governing plasmas are relatively simple, plasma behavior is extraordinarily varied and subtle: the emergence of unexpected behavior from a simple model is a typical feature of a complex system. Such systems lie in some sense on the boundary between ordered and disordered behavior and cannot typically be described either by simple, smooth, mathematical functions, or by pure randomness. The spontaneous formation of interesting spatial features on a wide range of length scales is one manifestation of plasma complexity. The features are interesting, for example, because they are very sharp, spatially intermittent (the distance between features is much larger than the features themselves), or have a fractal form. Many of these features were first studied in the laboratory, and have subsequently been recognized throughout the universe. Examples of complexity and complex structures in plasmas include:

FilamentationEdit

Striations or string-like structures,[45] also known as Birkeland currents, are seen in many plasmas, like the plasma ball, the aurora,[46] lightning,[47] electric arcs, solar flares,[48] and supernova remnants.[49] They are sometimes associated with larger current densities, and the interaction with the magnetic field can form a magnetic rope structure.[50] High power microwave breakdown at atmospheric pressure also leads to the formation of filamentary structures.[51] (See also Plasma pinch)

Filamentation also refers to the self-focusing of a high power laser pulse. At high powers, the nonlinear part of the index of refraction becomes important and causes a higher index of refraction in the center of the laser beam, where the laser is brighter than at the edges, causing a feedback that focuses the laser even more. The tighter focused laser has a higher peak brightness (irradiance) that forms a plasma. The plasma has an index of refraction lower than one, and causes a defocusing of the laser beam. The interplay of the focusing index of refraction, and the defocusing plasma makes the formation of a long filament of plasma that can be micrometers to kilometers in length.[52] One interesting aspect of the filamentation generated plasma is the relatively low ion density due to defocusing effects of the ionised electrons.[53] (See also Filament propagation)

Non-neutral plasmaEdit

The strength and range of the electric force and the good conductivity of plasmas usually ensure that the densities of positive and negative charges in any sizeable region are equal ("quasineutrality"). A plasma with a significant excess of charge density, or, in the extreme case, is composed of a single species, is called a non-neutral plasma. In such a plasma, electric fields play a dominant role. Examples are charged particle beams, an electron cloud in a Penning trap and positron plasmas.[54]

Dusty plasma/grain plasmaEdit

A dusty plasma contains tiny charged particles of dust (typically found in space). The dust particles acquire high charges and interact with each other. A plasma that contains larger particles is called grain plasma. Under laboratory conditions, dusty plasmas are also called complex plasmas.[55]

Impermeable plasmaEdit

Impermeable plasma is a type of thermal plasma which acts like an impermeable solid with respect to gas or cold plasma and can be physically pushed. Interaction of cold gas and thermal plasma was briefly studied by a group led by Hannes Alfvén in 1960s and 1970s for its possible applications in insulation of fusion plasma from the reactor walls.[56] However, later it was found that the external magnetic fields in this configuration could induce kink instabilities in the plasma and subsequently lead to an unexpectedly high heat loss to the walls.[57] In 2013, a group of materials scientists reported that they have successfully generated stable impermeable plasma with no magnetic confinement using only an ultrahigh-pressure blanket of cold gas. While spectroscopic data on the characteristics of plasma were claimed to be difficult to obtain due to the high pressure, the passive effect of plasma on synthesis of different nanostructures clearly suggested the effective confinement. They also showed that upon maintaining the impermeability for a few tens of seconds, screening of ions at the plasma-gas interface could give rise to a strong secondary mode of heating (known as viscous heating) leading to different kinetics of reactions and formation of complex nanomaterials.[58]

Mathematical descriptionsEdit

 
The complex self-constricting magnetic field lines and current paths in a field-aligned Birkeland current that can develop in a plasma.[59]

To completely describe the state of a plasma, all of the particle locations and velocities and describe the electromagnetic field in the plasma region would need to be written down. However, it is generally not practical or necessary to keep track of all the particles in a plasma. Therefore, plasma physicists commonly use less detailed descriptions, of which there are two main types:

Fluid modelEdit

Fluid models describe plasmas in terms of smoothed quantities, like density and averaged velocity around each position (see Plasma parameters). One simple fluid model, magnetohydrodynamics, treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier–Stokes equations. A more general description is the two-fluid plasma picture, where the ions and electrons are described separately. Fluid models are often accurate when collisionality is sufficiently high to keep the plasma velocity distribution close to a Maxwell–Boltzmann distribution. Because fluid models usually describe the plasma in terms of a single flow at a certain temperature at each spatial location, they can neither capture velocity space structures like beams or double layers, nor resolve wave-particle effects.

Kinetic modelEdit

Kinetic models describe the particle velocity distribution function at each point in the plasma and therefore do not need to assume a Maxwell–Boltzmann distribution. A kinetic description is often necessary for collisionless plasmas. There are two common approaches to kinetic description of a plasma. One is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, includes kinetic information by following the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models. The Vlasov equation may be used to describe the dynamics of a system of charged particles interacting with an electromagnetic field. In magnetized plasmas, a gyrokinetic approach can substantially reduce the computational expense of a fully kinetic simulation.

Artificial plasmasEdit

Most artificial plasmas are generated by the application of electric and/or magnetic fields through a gas. Plasma generated in a laboratory setting and for industrial use can be generally categorized by:

  • The type of power source used to generate the plasma—DC, RF and microwave
  • The pressure they operate at—vacuum pressure (< 10 mTorr or 1 Pa), moderate pressure (≈1 Torr or 100 Pa), atmospheric pressure (760 Torr or 100 kPa)
  • The degree of ionization within the plasma—fully, partially, or weakly ionised
  • The temperature relationships within the plasma—thermal plasma ( ), non-thermal or "cold" plasma ( )
  • The electrode configuration used to generate the plasma
  • The magnetization of the particles within the plasma—magnetized (both ion and electrons are trapped in Larmor orbits by the magnetic field), partially magnetized (the electrons but not the ions are trapped by the magnetic field), non-magnetized (the magnetic field is too weak to trap the particles in orbits but may generate Lorentz forces)[citation needed]

Generation of artificial plasmaEdit

 
Artificial plasma produced in air by a Jacob's Ladder

Just like the many uses of plasma, there are several means for its generation, however, one principle is common to all of them: there must be energy input to produce and sustain it.[60] For this case, plasma is generated when an electric current is applied across a dielectric gas or fluid (an electrically non-conducting material) as can be seen in the adjacent image, which shows a discharge tube as a simple example (DC used for simplicity).

The potential difference and subsequent electric field pull the bound electrons (negative) toward the anode (positive electrode) while the cathode (negative electrode) pulls the nucleus.[61] As the voltage increases, the current stresses the material (by electric polarization) beyond its dielectric limit (termed strength) into a stage of electrical breakdown, marked by an electric spark, where the material transforms from being an insulator into a conductor (as it becomes increasingly ionized). The underlying process is the Townsend avalanche, where collisions between electrons and neutral gas atoms create more ions and electrons (as can be seen in the figure on the right). The first impact of an electron on an atom results in one ion and two electrons. Therefore, the number of charged particles increases rapidly (in the millions) only "after about 20 successive sets of collisions",[62] mainly due to a small mean free path (average distance travelled between collisions).

Electric arcEdit

 
Cascade process of ionization. Electrons are ‘e−’, neutral atoms ‘o’, and cations ‘+’.
 
Avalanche effect between two electrodes. The original ionisation event liberates one electron, and each subsequent collision liberates a further electron, so two electrons emerge from each collision: the ionising electron and the liberated electron.

With ample current density and ionization, this forms a luminous electric arc (a continuous electric discharge similar to lightning) between the electrodes.[Note 1] Electrical resistance along the continuous electric arc creates heat, which dissociates more gas molecules and ionizes the resulting atoms (where degree of ionization is determined by temperature), and as per the sequence: solid-liquid-gas-plasma, the gas is gradually turned into a thermal plasma.[Note 2] A thermal plasma is in thermal equilibrium, which is to say that the temperature is relatively homogeneous throughout the heavy particles (i.e. atoms, molecules and ions) and electrons. This is so because when thermal plasmas are generated, electrical energy is given to electrons, which, due to their great mobility and large numbers, are able to disperse it rapidly and by elastic collision (without energy loss) to the heavy particles.[63][Note 3]

Examples of industrial/commercial plasmaEdit

Because of their sizable temperature and density ranges, plasmas find applications in many fields of research, technology and industry. For example, in: industrial and extractive metallurgy,[63] surface treatments such as plasma spraying (coating), etching in microelectronics,[64] metal cutting[65] and welding; as well as in everyday vehicle exhaust cleanup and fluorescent/luminescent lamps,[60] while even playing a part in supersonic combustion engines for aerospace engineering.[66]

Low-pressure dischargesEdit

  • Glow discharge plasmas: non-thermal plasmas generated by the application of DC or low frequency RF (<100 kHz) electric field to the gap between two metal electrodes. Probably the most common plasma; this is the type of plasma generated within fluorescent light tubes.[67]
  • Capacitively coupled plasma (CCP): similar to glow discharge plasmas, but generated with high frequency RF electric fields, typically 13.56 MHz. These differ from glow discharges in that the sheaths are much less intense. These are widely used in the microfabrication and integrated circuit manufacturing industries for plasma etching and plasma enhanced chemical vapor deposition.[68]
  • Cascaded Arc Plasma Source: a device to produce low temperature (≈1eV) high density plasmas (HDP).
  • Inductively coupled plasma (ICP): similar to a CCP and with similar applications but the electrode consists of a coil wrapped around the chamber where plasma is formed.[69]
  • Wave heated plasma: similar to CCP and ICP in that it is typically RF (or microwave). Examples include helicon discharge and electron cyclotron resonance (ECR).[70]

Atmospheric pressureEdit

  • Arc discharge: this is a high power thermal discharge of very high temperature (≈10,000 K). It can be generated using various power supplies. It is commonly used in metallurgical processes. For example, it is used to smelt minerals containing Al2O3 to produce aluminium.
  • Corona discharge: this is a non-thermal discharge generated by the application of high voltage to sharp electrode tips. It is commonly used in ozone generators and particle precipitators.
  • Dielectric barrier discharge (DBD): this is a non-thermal discharge generated by the application of high voltages across small gaps wherein a non-conducting coating prevents the transition of the plasma discharge into an arc. It is often mislabeled 'Corona' discharge in industry and has similar application to corona discharges. It is also widely used in the web treatment of fabrics.[71] The application of the discharge to synthetic fabrics and plastics functionalizes the surface and allows for paints, glues and similar materials to adhere.[72] The dielectric barrier discharge was used in the mid-1990s to show that low temperature atmospheric pressure plasma is effective in inactivating bacterial cells.[73] This work and later experiments using mammalian cells led to the establishment of a new field of research known as plasma medicine. The dielectric barrier discharge configuration was also used in the design of low temperature plasma jets. These plasma jets are produced by fast propagating guided ionization waves known as plasma bullets.[74]
  • Capacitive discharge: this is a nonthermal plasma generated by the application of RF power (e.g., 13.56 MHz) to one powered electrode, with a grounded electrode held at a small separation distance on the order of 1 cm. Such discharges are commonly stabilized using a noble gas such as helium or argon.[75]
  • "Piezoelectric direct discharge plasma:" is a nonthermal plasma generated at the high-side of a piezoelectric transformer (PT). This generation variant is particularly suited for high efficient and compact devices where a separate high voltage power supply is not desired.

ResearchEdit

Research examplesEdit

See alsoEdit

NotesEdit

  1. ^ The material undergoes various ‘regimes’ or stages (e.g. saturation, breakdown, glow, transition and thermal arc) as the voltage is increased under the voltage-current relationship. The voltage rises to its maximum value in the saturation stage, and thereafter it undergoes fluctuations of the various stages; while the current progressively increases throughout.[62]
  2. ^ Across literature, there appears to be no strict definition on where the boundary is between a gas and plasma. Nevertheless, it is enough to say that at 2,000°C the gas molecules become atomized, and ionised at 3,000 °C and "in this state, [the] gas has a liquid like viscosity at atmospheric pressure and the free electric charges confer relatively high electrical conductivities that can approach those of metals."[63]
  3. ^ Note that non-thermal, or non-equilibrium plasmas are not as ionised and have lower energy densities, and thus the temperature is not dispersed evenly among the particles, where some heavy ones remain ‘cold’.

ReferencesEdit

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